Phase retrieval is an image-based wavefront sensing method that utilizes point-source images or other known objects to recover optical phase information.
Conventional image-based phase retrieval techniques may be classified into two general categories: iterative-transform methods and parametric methods. Modifications to the original iterative-transform approach have been based on the introduction of a defocus diversity function or on the input-output method. Various implementations of the focus-diverse iterative-transform method have appeared that deviate slightly by utilizing a single wavelength or by varying the placement and number of defocused image planes. Modifications to the parametric approach include minimizing alternative merit functions as well as implementing a variety of nonlinear optimization methods such as Levenburg-Marquardt, simplex, and quasi-Newton techniques. The concept behind an optical diversity function is to modulate a point source image in a controlled way. The purpose of a diversity function in wavefront sensing is to “spread out” the optical response to expose aberration information. In principle, any known aberration can serve as a diversity function, but defocus is often the simplest to implement and exhibits no angular dependence as a function of the pupil coordinates. Since defocus has only angular dependence, no one part of the point spread function is emphasized more than any other.
The iterative-transform method can result in phase retrieval recoveries with higher spatial frequency content than is practical with parametric methods that solve directly for aberration coefficients of a given basis set, such as, for example, a Zernike basis set. From a different viewpoint, the method operation may be analyzed as consecutive projections onto convex sets. A disadvantage of the iterative-transform approach is that recovery results are prone to spurious phase values and branch points, as well as wrapped phase values for aberration contributions larger than one wave. As a result, it is well known that the iterative-transform method, while especially suited for high-spatial frequency phase recoveries, has a limited dynamic range when compared with the parameter-based approach, in which multi-wave recoveries are possible but are generally of lower spatial frequency. Multi-wave phase recoveries are possible, but generally require an additional phase-unwrapping post-processing step.
One particular approach is the Misell-Gerchberg-Saxton (MGS) method. The MGS approach is well suited for high spatial frequency phase map recoveries, but is not well suited for multi-wave recoveries, due to the well-known 2π phase wrapping problems inherent in the iterative-transform approach. Nevertheless, the MGS method approach can be utilized for multi-wave phase recoveries but requires an additional phase-unwrapping post-processing step.
For the reasons stated above, and for other reasons stated below, which will become apparent to those skilled in the art upon reading and understanding the present specification, there is a need in the art for alternative approaches for recovering aberrations in optical systems.